Let * be a binary operation on Z defined by a * b = a + b – 4 for all a, b ∈ Z. i. Show that ‘ * ’ is both commutative and associative. ii. Find the identity element in Z. iii. Find the invertible elements in Z Watch Solution
Let * be a binary operation on Q0 (Set of non-zero rational numbers) defined by a * b = 3ab/5 for all a, b ∈ Q0.Show that * is commutative as well as associative. Also, find its identity element, if it exists. Watch Solution
Let * be a binary operation on Q – {-1} defined by a * b = a + b + ab for all, a, b ∈ Q – {-1}. Then, i. Show that ‘ * ’ is both commutative and associative on Q – {-1}. ii. Find the identity element in Q – {-1}. iii. Show that every element of Q – {-1}. Is invertible. Also, find the inverse of an arbitrary element. Watch Solution
Let A = R0 x R, where R0 denote the set of all non-zero real numbers. A binary operation ‘O’ is defined on A as follows: (a, b) O (c, d) = (ac, bc + d) for all (a, b), (c, d) ∈ R0 x R. i. Show that ‘O’ is commutative and associative on A ii. Find the identity element in A iii. Find the invertible elements in A Watch Solution
Let ‘o’ be a binary operation on the set Q0 if all non – zero rational numbers defined by a o b = ab/2, for all a, b ∈ Q0. i. Show that ‘o’ is both commutative and associate. ii. Find the identity element in Q0. iii. Find the invertible elements of Q0. Watch Solution
On R – {1}, a binary operation * is defined by a * b = a + b – ab. Prove that * is commutative and associative. Find the identity element for * on R – {1}. Also, prove that every element of R – {1} is invertible. Watch Solution
Let R0 denote the set of all non – zero real numbers and let A=R0xR0. If ‘0’ is a binary operation on A defined by (a, b)0(c, d) = (ac, bd), (c, d)∈A. i. Show that ‘0’ is both commutative and associative on A ii. Find the identity element in A iii. Find the invertible element in A. Watch Solution
Let * be the binary operation on N defined by a * b = HCF of a and b. Does there exist identity for this binary operation on N? Watch Solution
Let A = RxR and * be a binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Show that * is commutative and associative. Find the binary element for * on A, if any. Watch Solution
